It is possible to impose structure on data. For example, while I said that you technically cannot use a mean for the one to five data at the ordinal scale, many statisticians would not have a problem using this number as a descriptor of the dataset.

The level at which you are interpreting data is a huge assumption that should be made at the beginning of any analysis. If you are looking at data that is generally thought of at the ordinal level and applying tools such as the arithmetic mean and standard deviation, this is something that data scientists must be aware of. This is mainly because if you continue to hold these assumptions as valid in your analysis, you may encounter problems. For example, if you also assume divisibility at the ordinal level by mistake, you are imposing structure where structure may not exist.